The invention relates to a process and an apparatus for coupling elastic and rigid contact line systems. For supplying power to electrically driven vehicles, particularly rail vehicles, contact lines are located in the form of wire arrangements suspended above the rail, wherein these wire arrangements direct electrical energy to the electrically driven vehicles via current collectors. The overhead contact wires are in accordance with European standards and each overhead contact wire is suspended on a catenary wire by means of suspension wires, suspended at short intervals, wherein the support points are located on the catenary wire approximately 30-180 cm higher than the overhead contact wire. The vertical distance from the rail to the support points is called the system height. For economic reasons, the system height must have very small dimensions inside tunnels and in the case of superstructures. Furthermore, the overhead contact wires and the catenary wires are mechanically tensioned at 8-30 kN in order to allow sliding friction contact speeds of up to 500 km/hr via the current collectors. The necessary tensioning devices are complex arrangements that are difficult to assemble, particularly in underground stretches of tunnel, since they require additional space. Furthermore, the current collector presses upward on the overhead contact wire at 70-300 N, which requires more space. For these reasons, for sites with limited space, such as in tunnels or superstructures, rigid contact rails were introduced, thus lowering the system height in particular. However, the transition from the elastic contact line to the rigid contact rail, i.e., the coupling between the contact line in the form of a hanging wire arrangement and the rigid contact rail, presents problems. It is customary to guide the overhead contact wire of the contact lines as a suspended wire arrangement parallel to the rigid contact rail. This, however, makes passage at high speeds more difficult and increases wear on the current collector. Furthermore, there is a danger of the current collector becoming entangled between the overhead contact wires and pulling the same down, which will bring the operation to a standstill.